On the size of a random sphere of influence graph

1999 ◽  
Vol 31 (3) ◽  
pp. 596-609 ◽  
Author(s):  
T. K. Chalker ◽  
A. P. Godbole ◽  
P. Hitczenko ◽  
J. Radcliff ◽  
O. G. Ruehr
Keyword(s):  
Upper And Lower Bounds ◽  
Exponential Inequality ◽  
Nearest Neighbour ◽  
Expected Number ◽  
Spheres Of Influence ◽  
Influence Graph ◽  
Influence Graphs ◽  
Sphere Of Influence ◽  
Proximity Graph ◽  
Sharp Concentration

We approach sphere of influence graphs (SIGs) from a probabilistic perspective. Ordinary SIGs were first introduced by Toussaint as a type of proximity graph for use in pattern recognition, computer vision and other low-level vision tasks. A random sphere of influence graph (RSIG) is constructed as follows. Consider n points uniformly and independently distributed within the unit square in d dimensions. Around each point, Xi, draw an open ball (‘sphere of influence’) with radius equal to the distance to Xi's nearest neighbour. Finally, draw an edge between two points if their spheres of influence intersect. Asymptotically exact values for the expected number of edges in a RSIG are determined for all values of d; previously, just upper and lower bounds were known for this quantity. A modification of the Azuma-Hoeffding exponential inequality is employed to exhibit the sharp concentration of the number of edges around its expected value.

On the size of a random sphere of influence graph

1999 ◽  
Vol 31 (03) ◽  
pp. 596-609 ◽  
Author(s):  
T. K. Chalker ◽  
A. P. Godbole ◽  
P. Hitczenko ◽  
J. Radcliff ◽  
O. G. Ruehr
Keyword(s):  
Upper And Lower Bounds ◽  
Exponential Inequality ◽  
Nearest Neighbour ◽  
Expected Number ◽  
Spheres Of Influence ◽  
Influence Graph ◽  
Influence Graphs ◽  
Sphere Of Influence ◽  
Proximity Graph ◽  
Sharp Concentration

We approach sphere of influence graphs (SIGs) from a probabilistic perspective. Ordinary SIGs were first introduced by Toussaint as a type of proximity graph for use in pattern recognition, computer vision and other low-level vision tasks. A random sphere of influence graph (RSIG) is constructed as follows. Consider n points uniformly and independently distributed within the unit square in d dimensions. Around each point, X i , draw an open ball (‘sphere of influence’) with radius equal to the distance to X i 's nearest neighbour. Finally, draw an edge between two points if their spheres of influence intersect. Asymptotically exact values for the expected number of edges in a RSIG are determined for all values of d; previously, just upper and lower bounds were known for this quantity. A modification of the Azuma-Hoeffding exponential inequality is employed to exhibit the sharp concentration of the number of edges around its expected value.

REMARKS ON THE SPHERE OF INFLUENCE GRAPH

1985 ◽  
Vol 440 (1 Discrete Geom) ◽  
pp. 323-327 ◽  
Author(s):  
David Avis ◽  
Joe Horton
Keyword(s):  
Influence Graph ◽  
Sphere Of Influence

Approximations to hard-core models and their application to statistical analysis

1982 ◽  
Vol 19 (A) ◽  
pp. 281-292 ◽  
Author(s):  
Mark Westcott
Keyword(s):  
Statistical Analysis ◽  
Statistical Inference ◽  
Lower Bounds ◽  
Hard Core ◽  
Distribution Functions ◽  
Core Model ◽  
Upper And Lower Bounds ◽  
Nearest Neighbour ◽  
Hard Core Model

This paper derives upper and lower bounds to the distribution functions of nearest-neighbour and minimum nearest-neighbour distances between N points generated by a hard-core model on the surface of a sphere. The use of these bounds in statistical inference is discussed.

Approximations to hard-core models and their application to statistical analysis

1982 ◽  
Vol 19 (A) ◽  
pp. 281-292 ◽  
Author(s):  
Mark Westcott
Keyword(s):  
Statistical Analysis ◽  
Statistical Inference ◽  
Lower Bounds ◽  
Hard Core ◽  
Distribution Functions ◽  
Core Model ◽  
Upper And Lower Bounds ◽  
Nearest Neighbour ◽  
Hard Core Model

This paper derives upper and lower bounds to the distribution functions of nearest-neighbour and minimum nearest-neighbour distances between N points generated by a hard-core model on the surface of a sphere. The use of these bounds in statistical inference is discussed.

scholarly journals A probabilistic analysis of the Fermi paradox in terms of the Drake formula: the role of the L factor

2020 ◽  
Vol 493 (3) ◽  
pp. 3464-3472 ◽  
Author(s):  
N Prantzos
Keyword(s):  
Parameter Space ◽  
Direct Contact ◽  
Future Research ◽  
Statistical Interpretation ◽  
Spheres Of Influence ◽  
The Galaxy ◽  
Technological Civilization ◽  
Sphere Of Influence ◽  
Practical Implications

ABSTRACT In evaluating the number of technological civilizations N in the Galaxy through the Drake formula, emphasis is mostly put on the astrophysical and biotechnological factors describing the emergence of a civilization and much less on its the lifetime, which is intimately related to its demise. It is argued here that this factor is in fact the most important regarding the practical implications of the Drake formula, because it determines the maximal extent of the ‘sphere of influence’ of any technological civilization. The Fermi paradox is studied in the terms of a simplified version of the Drake formula, through Monte Carlo simulations of N civilizations expanding in the Galaxy during their space faring lifetime L. In the framework of that scheme, the probability of ‘direct contact’ is determined as the fraction of the Galactic volume occupied collectively by the ‘spheres of influence’ of N civilizations. The results of the analysis are used to determine regions in the parameter space where the Fermi paradox holds. It is argued that in a large region of the diagram the corresponding parameters suggest rather a ‘weak’ Fermi paradox. Future research may reveal whether a ‘strong’ paradox holds in some part of the parameter space. Finally, it is argued that the value of N is not bound by N = 1 from below, contrary to what is usually assumed, but it may have a statistical interpretation.

Spheres of Influence: An Aspect of Semi-Suzerainty

1926 ◽  
Vol 20 (2) ◽  
pp. 300-325 ◽  
Author(s):  
Geddes W. Rutherford
Keyword(s):  
Great Britain ◽  
Central America ◽  
Foreign Affairs ◽  
House Of Commons ◽  
Precise Meaning ◽  
Spheres Of Influence ◽  
The Caribbean ◽  
Sphere Of Influence

Austen Chamberlain, British Secretary of Foreign Affairs, declared in the House of Commons, December 15, 1924, that Great Britain would “ regard as an unfriendly act any attempt at interference in the affairs of Egypt by any other Power, and would consider any aggression against the territory of Egypt as an act to be repelled with all the means at their command.” Similar statements have frequently been made by the responsible ministers of the Powers when discussing “ spheres of influence.” It is probably not possible to give a precise meaning to the phrase “ sphere of influence” because, as Hall says, “ perhaps in its indefiniteness consists its international value.” Nevertheless, the phrase has been applied specifically to characterize the control of portions of Asia and Africa, certain islands in the Caribbean, and of regions in Central America. In these regions are to be found in operation arrangements, some secret and some public, stipulated either by treaty, diplomatic declaration, “ gentlemen's agreements,” or effected, ofttimes, by military or economic penetration, varying greatly in degree and intensity, which enable Powers and their citizens to enjoy advantages in these regions without exercising, necessarily, sovereign control.

Understanding spheres of influence in international politics

2019 ◽  
Vol 5 (3) ◽  
pp. 255-273 ◽  
Author(s):  
Van Jackson
Keyword(s):  
International Relations ◽  
Ideal Type ◽  
Distinct Form ◽  
Relational Structures ◽  
Spheres Of Influence ◽  
Theoretical Perspectives ◽  
History Of ◽  
Sphere Of Influence ◽  
Do So ◽  
Type Hierarchy

AbstractSpheres of influence remain one of the most pervasive phenomena in the practice and history of international relations, yet only rarely have they been taken up analytically. To bring conceptual and discursive clarity, this article advances two arguments. First, it argues that spheres of influence are not a distinct form of hierarchy in international relations, but rather practices of control and exclusion that can be found within any ideal-type hierarchy. Second, these hierarchical practices are generally underspecified by those invoking the term. Different theoretical perspectives on international relations offer highly divergent ways of understanding control and exclusion, and all do so with plausible empirical mooring. Spheres of influence do not themselves denote a form of governance even if it does a form of order construction and maintenance. Any given empire, hegemonic order, or alliance may also be a sphere of influence depending on the practices that occur; the key is not to identify whether particular hierarchical traits are dispositive of one of these relational structures, but rather whether, and the extent to which, assertions of control and exclusion define the hierarchy.

scholarly journals Abstract sphere-of-influence graphs

1993 ◽  
Vol 17 (11) ◽  
pp. 77-83 ◽  
Author(s):  
Frank Harary ◽  
Michael S. Jacobson ◽  
Marc J. Lipman ◽  
F.R. McMorris
Keyword(s):  
Influence Graphs ◽  
Sphere Of Influence
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